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sggev.f(3)				      LAPACK				       sggev.f(3)

NAME
       sggev.f -

SYNOPSIS
   Functions/Subroutines
       subroutine sggev (JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VL, LDVL, VR,
	   LDVR, WORK, LWORK, INFO)
	    SGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors
	   for GE matrices

Function/Subroutine Documentation
   subroutine sggev (characterJOBVL, characterJOBVR, integerN, real, dimension( lda, * )A,
       integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( * )ALPHAR, real,
       dimension( * )ALPHAI, real, dimension( * )BETA, real, dimension( ldvl, * )VL, integerLDVL,
       real, dimension( ldvr, * )VR, integerLDVR, real, dimension( * )WORK, integerLWORK,
       integerINFO)
	SGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE
       matrices

       Purpose:

	    SGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B)
	    the generalized eigenvalues, and optionally, the left and/or right
	    generalized eigenvectors.

	    A generalized eigenvalue for a pair of matrices (A,B) is a scalar
	    lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
	    singular. It is usually represented as the pair (alpha,beta), as
	    there is a reasonable interpretation for beta=0, and even for both
	    being zero.

	    The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
	    of (A,B) satisfies

			     A * v(j) = lambda(j) * B * v(j).

	    The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
	    of (A,B) satisfies

			     u(j)**H * A  = lambda(j) * u(j)**H * B .

	    where u(j)**H is the conjugate-transpose of u(j).

       Parameters:
	   JOBVL

		     JOBVL is CHARACTER*1
		     = 'N':  do not compute the left generalized eigenvectors;
		     = 'V':  compute the left generalized eigenvectors.

	   JOBVR

		     JOBVR is CHARACTER*1
		     = 'N':  do not compute the right generalized eigenvectors;
		     = 'V':  compute the right generalized eigenvectors.

	   N

		     N is INTEGER
		     The order of the matrices A, B, VL, and VR.  N >= 0.

	   A

		     A is REAL array, dimension (LDA, N)
		     On entry, the matrix A in the pair (A,B).
		     On exit, A has been overwritten.

	   LDA

		     LDA is INTEGER
		     The leading dimension of A.  LDA >= max(1,N).

	   B

		     B is REAL array, dimension (LDB, N)
		     On entry, the matrix B in the pair (A,B).
		     On exit, B has been overwritten.

	   LDB

		     LDB is INTEGER
		     The leading dimension of B.  LDB >= max(1,N).

	   ALPHAR

		     ALPHAR is REAL array, dimension (N)

	   ALPHAI

		     ALPHAI is REAL array, dimension (N)

	   BETA

		     BETA is REAL array, dimension (N)
		     On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
		     be the generalized eigenvalues.  If ALPHAI(j) is zero, then
		     the j-th eigenvalue is real; if positive, then the j-th and
		     (j+1)-st eigenvalues are a complex conjugate pair, with
		     ALPHAI(j+1) negative.

		     Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
		     may easily over- or underflow, and BETA(j) may even be zero.
		     Thus, the user should avoid naively computing the ratio
		     alpha/beta.  However, ALPHAR and ALPHAI will be always less
		     than and usually comparable with norm(A) in magnitude, and
		     BETA always less than and usually comparable with norm(B).

	   VL

		     VL is REAL array, dimension (LDVL,N)
		     If JOBVL = 'V', the left eigenvectors u(j) are stored one
		     after another in the columns of VL, in the same order as
		     their eigenvalues. If the j-th eigenvalue is real, then
		     u(j) = VL(:,j), the j-th column of VL. If the j-th and
		     (j+1)-th eigenvalues form a complex conjugate pair, then
		     u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1).
		     Each eigenvector is scaled so the largest component has
		     abs(real part)+abs(imag. part)=1.
		     Not referenced if JOBVL = 'N'.

	   LDVL

		     LDVL is INTEGER
		     The leading dimension of the matrix VL. LDVL >= 1, and
		     if JOBVL = 'V', LDVL >= N.

	   VR

		     VR is REAL array, dimension (LDVR,N)
		     If JOBVR = 'V', the right eigenvectors v(j) are stored one
		     after another in the columns of VR, in the same order as
		     their eigenvalues. If the j-th eigenvalue is real, then
		     v(j) = VR(:,j), the j-th column of VR. If the j-th and
		     (j+1)-th eigenvalues form a complex conjugate pair, then
		     v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1).
		     Each eigenvector is scaled so the largest component has
		     abs(real part)+abs(imag. part)=1.
		     Not referenced if JOBVR = 'N'.

	   LDVR

		     LDVR is INTEGER
		     The leading dimension of the matrix VR. LDVR >= 1, and
		     if JOBVR = 'V', LDVR >= N.

	   WORK

		     WORK is REAL array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

	   LWORK

		     LWORK is INTEGER
		     The dimension of the array WORK.  LWORK >= max(1,8*N).
		     For good performance, LWORK must generally be larger.

		     If LWORK = -1, then a workspace query is assumed; the routine
		     only calculates the optimal size of the WORK array, returns
		     this value as the first entry of the WORK array, and no error
		     message related to LWORK is issued by XERBLA.

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value.
		     = 1,...,N:
			   The QZ iteration failed.  No eigenvectors have been
			   calculated, but ALPHAR(j), ALPHAI(j), and BETA(j)
			   should be correct for j=INFO+1,...,N.
		     > N:  =N+1: other than QZ iteration failed in SHGEQZ.
			   =N+2: error return from STGEVC.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   April 2012

       Definition at line 226 of file sggev.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			       sggev.f(3)
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